论文标题
数据驱动的分布在具有不确定动态的系统的功能强大的MPC
Data-driven distributionally robust MPC for systems with uncertain dynamics
论文作者
论文摘要
我们提供了一个新型的数据驱动的分布在稳健的模型模型预测控制公式，该模型对未知和可能不受限制的添加剂不确定性影响的未知离散时间线性时间流动系统。我们使用离线收集的数据和动力学的近似模型来制定有限的摩尼子优化问题。为了说明与系统上作用的动态和干扰有关的不确定性，我们诉诸于分布强劲的公式，以优化成本期望，同时满足使用Wasserstein Metric定义的模棱两可的不确定性中最差的不确定性概率分布的条件价值约束。使用分布强大的优化文献中的结果，我们得出了一个可拖动的有限维凸优化问题，并提供了有限样本的保证，用于凸面分段仿射成本和约束功能。在一个简单的数值示例中，在闭环模拟中证明了所提出的算法的性能。
We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected data and an approximate model of the dynamics to formulate a finite-horizon optimization problem. To account for both the uncertainty related to the dynamics and the disturbance acting on the system, we resort to a distributionally robust formulation that optimizes the cost expectation while satisfying Conditional Value-at-Risk constraints with respect to the worst-case probability distributions of the uncertainties within an ambiguity set defined using the Wasserstein metric. Using results from the distributionally robust optimization literature we derive a tractable finite-dimensional convex optimization problem with finite-sample guarantees for the class of convex piecewise affine cost and constraint functions. The performance of the proposed algorithm is demonstrated in closed-loop simulation on a simple numerical example.
